{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import all libraries for the rest of the blog post\n",
    "from scipy.integrate import quad\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Polygon\n",
    "import scipy.stats as stats\n",
    "import pandas as pd\n",
    "\n",
    "# This is needed for z table formatting\n",
    "pd.options.display.float_format = '{:<.4f}'.format\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to use a Z Table\n",
    "\n",
    "SAT (out of 1600) score ~ N(mean = 1000, SD = 150) <br>\n",
    "ACT scores ~ N(mean = 20, SD = 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### SAT Score (numbers are faked)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mu, sigma = 1000, 150 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 100000)\n",
    "\n",
    "h = sorted(s)\n",
    "\n",
    "fit = stats.norm.pdf(h, np.mean(h), np.std(h))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 5), frameon=False);\n",
    "ax.plot(h, fit, 'k', linewidth=1.2);\n",
    "ax.set_ylim(bottom=0);\n",
    "ax.set_xlim(400, 1600);\n",
    "\n",
    "df = pd.DataFrame(list(zip(h, fit)), columns = ['score', 'integral'])\n",
    "df[(df['score'] >= 1149.90) & (df['score'] <= 1150.10) ].values.tolist()\n",
    "\n",
    "# Make the shaded region\n",
    "verts = [(1149.90, 0)] + df[(df['score'] >= 1149.90) & (df['score'] <= 1150.10) ].values.tolist() + [(1150.1, 0)]\n",
    "poly = Polygon(verts, facecolor='green', edgecolor='r', alpha = 1, linewidth = 1.2, linestyle = '-')\n",
    "ax.add_patch(poly);\n",
    "plt.xticks(fontsize = 22)\n",
    "ax.set_xlabel('SAT Score (Mike)', fontsize = 28)\n",
    "\n",
    "ax.set_frame_on(False)\n",
    "ax.axhline(0, c = 'k', linewidth = 3)\n",
    "ax.get_yaxis().set_visible(False)\n",
    "ax.text(1150,.0005, '1150', horizontalalignment='center', fontsize=22,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'black', 'pad':5});\n",
    "plt.tight_layout()\n",
    "fig.savefig('SAT_Mike.png', dpi = 900)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ACT Score (numbers are faked)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mu, sigma = 20, 4 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 100000)\n",
    "\n",
    "h = sorted(s)\n",
    "\n",
    "fit = stats.norm.pdf(h, np.mean(h), np.std(h))  #this is a fitting indeed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 5), frameon=False);\n",
    "ax.plot(h, fit, 'k', linewidth=1.2);\n",
    "ax.set_ylim(bottom=0);\n",
    "ax.set_xlim(4, 36);\n",
    "\n",
    "df = pd.DataFrame(list(zip(h, fit)), columns = ['score', 'integral'])\n",
    "df[(df['score'] >= 24.99733333333333) & (df['score'] <= 25.002666666666666) ].values.tolist()\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(25, 25, num = 1)\n",
    "verts = [(24.99733333333333, 0)] + df[(df['score'] >= 24.99733333333333) & (df['score'] <= 25.002666666666666) ].values.tolist() + [(25.002666666666666, 0)]\n",
    "poly = Polygon(verts, facecolor='green', edgecolor='b', alpha = 1, linewidth = 1.2, linestyle = '-')\n",
    "ax.add_patch(poly);\n",
    "ax.set_xticks(list(range(4, 40, 4)))\n",
    "plt.xticks(fontsize = 22)\n",
    "ax.set_xlabel('ACT Score (Zoe)', fontsize = 27)\n",
    "\n",
    "ax.set_frame_on(False)\n",
    "ax.axhline(0, c = 'k', linewidth = 3)\n",
    "ax.get_yaxis().set_visible(False)\n",
    "\n",
    "ax.text(25,.015, '25', horizontalalignment='center', fontsize=22,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'black', 'pad':5});\n",
    "plt.tight_layout()\n",
    "fig.savefig('ACT_Zoe.png', dpi = 900)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Z-Score Calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "zoe_z_score = (25 - 20) / 4.0\n",
    "mike_z_score = (1150 - 1000) / 150.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.25"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zoe_z_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mike_z_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Z-Score Table Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mu, sigma = 0, 1 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 1000000)\n",
    "\n",
    "h = sorted(s)\n",
    "\n",
    "fit = stats.norm.pdf(h, np.mean(h), np.std(h))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 5), frameon=False);\n",
    "ax.plot(h, fit, 'k', linewidth=1.2);\n",
    "ax.set_ylim(bottom=0);\n",
    "ax.set_xlim(-4, 4);\n",
    "\n",
    "df = pd.DataFrame(list(zip(h, fit)), columns = ['score', 'integral'])\n",
    "df[(df['score'] >= .99) & (df['score'] <= 1.01) ].values.tolist()\n",
    "\n",
    "# Make the shaded region\n",
    "verts = [(.99, 0)] + df[(df['score'] >= .99) & (df['score'] <= 1.01) ].values.tolist() + [(1.01, 0)]\n",
    "poly = Polygon(verts, facecolor='green', edgecolor='gray', alpha = 1, linewidth = 1.2, linestyle = '-')\n",
    "ax.add_patch(poly);\n",
    "\n",
    "# This is to make the second highlighted region\n",
    "\n",
    "scores_below_1 = df[(df['score'] >= -4) & (df['score'] <= 1) ].values.tolist()\n",
    "\n",
    "\n",
    "second_vert = [(-4, 0)] + scores_below_1 + [(1, 0)]\n",
    "poly2 = Polygon(second_vert, facecolor='gray', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly2);\n",
    "\n",
    "\n",
    "plt.xticks(fontsize = 22)\n",
    "#ax.set_xlabel('SAT Score (Mike)', fontsize = 28)\n",
    "\n",
    "ax.set_frame_on(False)\n",
    "ax.axhline(0, c = 'k', linewidth = 3)\n",
    "ax.get_yaxis().set_visible(False)\n",
    "#ax.text(1150,.0005, '1150', horizontalalignment='center', fontsize=22,\n",
    "#            bbox={'facecolor':'white', 'edgecolor':'black', 'pad':5});\n",
    "plt.tight_layout()\n",
    "xticklabels = ['', '', '', '', '0', 'z', '', '', '']\n",
    "ax.set_xticklabels(xticklabels, fontsize = 32)\n",
    "fig.savefig('standardNormalPositiveZScores.png', dpi = 900)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cumulative Distribution Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Math Expression</b> $$\\int_{-\\infty}^{z}\\frac{1}{\\sqrt{2\\pi}}e^{-x^{2}/2}\\mathrm{d}x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Zoe:  0.894350226333146\n",
      "Mike:  0.8413447460685435\n"
     ]
    }
   ],
   "source": [
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )\n",
    "\n",
    "zoe_percentile, _ = quad(normalProbabilityDensity, np.NINF, 1.25)\n",
    "mike_percentile, _ = quad(normalProbabilityDensity, np.NINF, 1.00)\n",
    "print('Zoe: ', zoe_percentile)\n",
    "print('Mike: ', mike_percentile)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate Standard Normal Table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "standard_normal_table = pd.DataFrame(data = [],\n",
    "                                     index = np.round(np.arange(0, 3.5, .1),2),\n",
    "                                     columns = np.round(np.arange(0.00, .1, .01), 2))\n",
    "\n",
    "for index in standard_normal_table.index:\n",
    "    for column in standard_normal_table.columns:\n",
    "        z = np.round(index + column, 2)\n",
    "        value, _ = quad(normalProbabilityDensity, np.NINF, z)\n",
    "        standard_normal_table.loc[index, column] = value\n",
    "\n",
    "standard_normal_table.index = standard_normal_table.index.astype(str)\n",
    "standard_normal_table.columns = [str(column).ljust(4,'0') for column in standard_normal_table.columns]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0.00</th>\n",
       "      <th>0.01</th>\n",
       "      <th>0.02</th>\n",
       "      <th>0.03</th>\n",
       "      <th>0.04</th>\n",
       "      <th>0.05</th>\n",
       "      <th>0.06</th>\n",
       "      <th>0.07</th>\n",
       "      <th>0.08</th>\n",
       "      <th>0.09</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.0</th>\n",
       "      <td>0.5000</td>\n",
       "      <td>0.5040</td>\n",
       "      <td>0.5080</td>\n",
       "      <td>0.5120</td>\n",
       "      <td>0.5160</td>\n",
       "      <td>0.5199</td>\n",
       "      <td>0.5239</td>\n",
       "      <td>0.5279</td>\n",
       "      <td>0.5319</td>\n",
       "      <td>0.5359</td>\n",
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       "    <tr>\n",
       "      <th>0.1</th>\n",
       "      <td>0.5398</td>\n",
       "      <td>0.5438</td>\n",
       "      <td>0.5478</td>\n",
       "      <td>0.5517</td>\n",
       "      <td>0.5557</td>\n",
       "      <td>0.5596</td>\n",
       "      <td>0.5636</td>\n",
       "      <td>0.5675</td>\n",
       "      <td>0.5714</td>\n",
       "      <td>0.5753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.2</th>\n",
       "      <td>0.5793</td>\n",
       "      <td>0.5832</td>\n",
       "      <td>0.5871</td>\n",
       "      <td>0.5910</td>\n",
       "      <td>0.5948</td>\n",
       "      <td>0.5987</td>\n",
       "      <td>0.6026</td>\n",
       "      <td>0.6064</td>\n",
       "      <td>0.6103</td>\n",
       "      <td>0.6141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.3</th>\n",
       "      <td>0.6179</td>\n",
       "      <td>0.6217</td>\n",
       "      <td>0.6255</td>\n",
       "      <td>0.6293</td>\n",
       "      <td>0.6331</td>\n",
       "      <td>0.6368</td>\n",
       "      <td>0.6406</td>\n",
       "      <td>0.6443</td>\n",
       "      <td>0.6480</td>\n",
       "      <td>0.6517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.4</th>\n",
       "      <td>0.6554</td>\n",
       "      <td>0.6591</td>\n",
       "      <td>0.6628</td>\n",
       "      <td>0.6664</td>\n",
       "      <td>0.6700</td>\n",
       "      <td>0.6736</td>\n",
       "      <td>0.6772</td>\n",
       "      <td>0.6808</td>\n",
       "      <td>0.6844</td>\n",
       "      <td>0.6879</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.5</th>\n",
       "      <td>0.6915</td>\n",
       "      <td>0.6950</td>\n",
       "      <td>0.6985</td>\n",
       "      <td>0.7019</td>\n",
       "      <td>0.7054</td>\n",
       "      <td>0.7088</td>\n",
       "      <td>0.7123</td>\n",
       "      <td>0.7157</td>\n",
       "      <td>0.7190</td>\n",
       "      <td>0.7224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.6</th>\n",
       "      <td>0.7257</td>\n",
       "      <td>0.7291</td>\n",
       "      <td>0.7324</td>\n",
       "      <td>0.7357</td>\n",
       "      <td>0.7389</td>\n",
       "      <td>0.7422</td>\n",
       "      <td>0.7454</td>\n",
       "      <td>0.7486</td>\n",
       "      <td>0.7517</td>\n",
       "      <td>0.7549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.7</th>\n",
       "      <td>0.7580</td>\n",
       "      <td>0.7611</td>\n",
       "      <td>0.7642</td>\n",
       "      <td>0.7673</td>\n",
       "      <td>0.7704</td>\n",
       "      <td>0.7734</td>\n",
       "      <td>0.7764</td>\n",
       "      <td>0.7794</td>\n",
       "      <td>0.7823</td>\n",
       "      <td>0.7852</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.8</th>\n",
       "      <td>0.7881</td>\n",
       "      <td>0.7910</td>\n",
       "      <td>0.7939</td>\n",
       "      <td>0.7967</td>\n",
       "      <td>0.7995</td>\n",
       "      <td>0.8023</td>\n",
       "      <td>0.8051</td>\n",
       "      <td>0.8078</td>\n",
       "      <td>0.8106</td>\n",
       "      <td>0.8133</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.9</th>\n",
       "      <td>0.8159</td>\n",
       "      <td>0.8186</td>\n",
       "      <td>0.8212</td>\n",
       "      <td>0.8238</td>\n",
       "      <td>0.8264</td>\n",
       "      <td>0.8289</td>\n",
       "      <td>0.8315</td>\n",
       "      <td>0.8340</td>\n",
       "      <td>0.8365</td>\n",
       "      <td>0.8389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>0.8413</td>\n",
       "      <td>0.8438</td>\n",
       "      <td>0.8461</td>\n",
       "      <td>0.8485</td>\n",
       "      <td>0.8508</td>\n",
       "      <td>0.8531</td>\n",
       "      <td>0.8554</td>\n",
       "      <td>0.8577</td>\n",
       "      <td>0.8599</td>\n",
       "      <td>0.8621</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.1</th>\n",
       "      <td>0.8643</td>\n",
       "      <td>0.8665</td>\n",
       "      <td>0.8686</td>\n",
       "      <td>0.8708</td>\n",
       "      <td>0.8729</td>\n",
       "      <td>0.8749</td>\n",
       "      <td>0.8770</td>\n",
       "      <td>0.8790</td>\n",
       "      <td>0.8810</td>\n",
       "      <td>0.8830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.2</th>\n",
       "      <td>0.8849</td>\n",
       "      <td>0.8869</td>\n",
       "      <td>0.8888</td>\n",
       "      <td>0.8907</td>\n",
       "      <td>0.8925</td>\n",
       "      <td>0.8944</td>\n",
       "      <td>0.8962</td>\n",
       "      <td>0.8980</td>\n",
       "      <td>0.8997</td>\n",
       "      <td>0.9015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.3</th>\n",
       "      <td>0.9032</td>\n",
       "      <td>0.9049</td>\n",
       "      <td>0.9066</td>\n",
       "      <td>0.9082</td>\n",
       "      <td>0.9099</td>\n",
       "      <td>0.9115</td>\n",
       "      <td>0.9131</td>\n",
       "      <td>0.9147</td>\n",
       "      <td>0.9162</td>\n",
       "      <td>0.9177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.4</th>\n",
       "      <td>0.9192</td>\n",
       "      <td>0.9207</td>\n",
       "      <td>0.9222</td>\n",
       "      <td>0.9236</td>\n",
       "      <td>0.9251</td>\n",
       "      <td>0.9265</td>\n",
       "      <td>0.9279</td>\n",
       "      <td>0.9292</td>\n",
       "      <td>0.9306</td>\n",
       "      <td>0.9319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.5</th>\n",
       "      <td>0.9332</td>\n",
       "      <td>0.9345</td>\n",
       "      <td>0.9357</td>\n",
       "      <td>0.9370</td>\n",
       "      <td>0.9382</td>\n",
       "      <td>0.9394</td>\n",
       "      <td>0.9406</td>\n",
       "      <td>0.9418</td>\n",
       "      <td>0.9429</td>\n",
       "      <td>0.9441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.6</th>\n",
       "      <td>0.9452</td>\n",
       "      <td>0.9463</td>\n",
       "      <td>0.9474</td>\n",
       "      <td>0.9484</td>\n",
       "      <td>0.9495</td>\n",
       "      <td>0.9505</td>\n",
       "      <td>0.9515</td>\n",
       "      <td>0.9525</td>\n",
       "      <td>0.9535</td>\n",
       "      <td>0.9545</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.7</th>\n",
       "      <td>0.9554</td>\n",
       "      <td>0.9564</td>\n",
       "      <td>0.9573</td>\n",
       "      <td>0.9582</td>\n",
       "      <td>0.9591</td>\n",
       "      <td>0.9599</td>\n",
       "      <td>0.9608</td>\n",
       "      <td>0.9616</td>\n",
       "      <td>0.9625</td>\n",
       "      <td>0.9633</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.8</th>\n",
       "      <td>0.9641</td>\n",
       "      <td>0.9649</td>\n",
       "      <td>0.9656</td>\n",
       "      <td>0.9664</td>\n",
       "      <td>0.9671</td>\n",
       "      <td>0.9678</td>\n",
       "      <td>0.9686</td>\n",
       "      <td>0.9693</td>\n",
       "      <td>0.9699</td>\n",
       "      <td>0.9706</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.9</th>\n",
       "      <td>0.9713</td>\n",
       "      <td>0.9719</td>\n",
       "      <td>0.9726</td>\n",
       "      <td>0.9732</td>\n",
       "      <td>0.9738</td>\n",
       "      <td>0.9744</td>\n",
       "      <td>0.9750</td>\n",
       "      <td>0.9756</td>\n",
       "      <td>0.9761</td>\n",
       "      <td>0.9767</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>0.9772</td>\n",
       "      <td>0.9778</td>\n",
       "      <td>0.9783</td>\n",
       "      <td>0.9788</td>\n",
       "      <td>0.9793</td>\n",
       "      <td>0.9798</td>\n",
       "      <td>0.9803</td>\n",
       "      <td>0.9808</td>\n",
       "      <td>0.9812</td>\n",
       "      <td>0.9817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.1</th>\n",
       "      <td>0.9821</td>\n",
       "      <td>0.9826</td>\n",
       "      <td>0.9830</td>\n",
       "      <td>0.9834</td>\n",
       "      <td>0.9838</td>\n",
       "      <td>0.9842</td>\n",
       "      <td>0.9846</td>\n",
       "      <td>0.9850</td>\n",
       "      <td>0.9854</td>\n",
       "      <td>0.9857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.2</th>\n",
       "      <td>0.9861</td>\n",
       "      <td>0.9864</td>\n",
       "      <td>0.9868</td>\n",
       "      <td>0.9871</td>\n",
       "      <td>0.9875</td>\n",
       "      <td>0.9878</td>\n",
       "      <td>0.9881</td>\n",
       "      <td>0.9884</td>\n",
       "      <td>0.9887</td>\n",
       "      <td>0.9890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.3</th>\n",
       "      <td>0.9893</td>\n",
       "      <td>0.9896</td>\n",
       "      <td>0.9898</td>\n",
       "      <td>0.9901</td>\n",
       "      <td>0.9904</td>\n",
       "      <td>0.9906</td>\n",
       "      <td>0.9909</td>\n",
       "      <td>0.9911</td>\n",
       "      <td>0.9913</td>\n",
       "      <td>0.9916</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.4</th>\n",
       "      <td>0.9918</td>\n",
       "      <td>0.9920</td>\n",
       "      <td>0.9922</td>\n",
       "      <td>0.9925</td>\n",
       "      <td>0.9927</td>\n",
       "      <td>0.9929</td>\n",
       "      <td>0.9931</td>\n",
       "      <td>0.9932</td>\n",
       "      <td>0.9934</td>\n",
       "      <td>0.9936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.5</th>\n",
       "      <td>0.9938</td>\n",
       "      <td>0.9940</td>\n",
       "      <td>0.9941</td>\n",
       "      <td>0.9943</td>\n",
       "      <td>0.9945</td>\n",
       "      <td>0.9946</td>\n",
       "      <td>0.9948</td>\n",
       "      <td>0.9949</td>\n",
       "      <td>0.9951</td>\n",
       "      <td>0.9952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.6</th>\n",
       "      <td>0.9953</td>\n",
       "      <td>0.9955</td>\n",
       "      <td>0.9956</td>\n",
       "      <td>0.9957</td>\n",
       "      <td>0.9959</td>\n",
       "      <td>0.9960</td>\n",
       "      <td>0.9961</td>\n",
       "      <td>0.9962</td>\n",
       "      <td>0.9963</td>\n",
       "      <td>0.9964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.7</th>\n",
       "      <td>0.9965</td>\n",
       "      <td>0.9966</td>\n",
       "      <td>0.9967</td>\n",
       "      <td>0.9968</td>\n",
       "      <td>0.9969</td>\n",
       "      <td>0.9970</td>\n",
       "      <td>0.9971</td>\n",
       "      <td>0.9972</td>\n",
       "      <td>0.9973</td>\n",
       "      <td>0.9974</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.8</th>\n",
       "      <td>0.9974</td>\n",
       "      <td>0.9975</td>\n",
       "      <td>0.9976</td>\n",
       "      <td>0.9977</td>\n",
       "      <td>0.9977</td>\n",
       "      <td>0.9978</td>\n",
       "      <td>0.9979</td>\n",
       "      <td>0.9979</td>\n",
       "      <td>0.9980</td>\n",
       "      <td>0.9981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.9</th>\n",
       "      <td>0.9981</td>\n",
       "      <td>0.9982</td>\n",
       "      <td>0.9982</td>\n",
       "      <td>0.9983</td>\n",
       "      <td>0.9984</td>\n",
       "      <td>0.9984</td>\n",
       "      <td>0.9985</td>\n",
       "      <td>0.9985</td>\n",
       "      <td>0.9986</td>\n",
       "      <td>0.9986</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>0.9987</td>\n",
       "      <td>0.9987</td>\n",
       "      <td>0.9987</td>\n",
       "      <td>0.9988</td>\n",
       "      <td>0.9988</td>\n",
       "      <td>0.9989</td>\n",
       "      <td>0.9989</td>\n",
       "      <td>0.9989</td>\n",
       "      <td>0.9990</td>\n",
       "      <td>0.9990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.1</th>\n",
       "      <td>0.9990</td>\n",
       "      <td>0.9991</td>\n",
       "      <td>0.9991</td>\n",
       "      <td>0.9991</td>\n",
       "      <td>0.9992</td>\n",
       "      <td>0.9992</td>\n",
       "      <td>0.9992</td>\n",
       "      <td>0.9992</td>\n",
       "      <td>0.9993</td>\n",
       "      <td>0.9993</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.2</th>\n",
       "      <td>0.9993</td>\n",
       "      <td>0.9993</td>\n",
       "      <td>0.9994</td>\n",
       "      <td>0.9994</td>\n",
       "      <td>0.9994</td>\n",
       "      <td>0.9994</td>\n",
       "      <td>0.9994</td>\n",
       "      <td>0.9995</td>\n",
       "      <td>0.9995</td>\n",
       "      <td>0.9995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.3</th>\n",
       "      <td>0.9995</td>\n",
       "      <td>0.9995</td>\n",
       "      <td>0.9995</td>\n",
       "      <td>0.9996</td>\n",
       "      <td>0.9996</td>\n",
       "      <td>0.9996</td>\n",
       "      <td>0.9996</td>\n",
       "      <td>0.9996</td>\n",
       "      <td>0.9996</td>\n",
       "      <td>0.9997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.4</th>\n",
       "      <td>0.9997</td>\n",
       "      <td>0.9997</td>\n",
       "      <td>0.9997</td>\n",
       "      <td>0.9997</td>\n",
       "      <td>0.9997</td>\n",
       "      <td>0.9997</td>\n",
       "      <td>0.9997</td>\n",
       "      <td>0.9997</td>\n",
       "      <td>0.9997</td>\n",
       "      <td>0.9998</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      0.00   0.01   0.02   0.03   0.04   0.05   0.06   0.07   0.08   0.09\n",
       "0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359\n",
       "0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753\n",
       "0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141\n",
       "0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517\n",
       "0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879\n",
       "0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224\n",
       "0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549\n",
       "0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852\n",
       "0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133\n",
       "0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389\n",
       "1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621\n",
       "1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830\n",
       "1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015\n",
       "1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177\n",
       "1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319\n",
       "1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441\n",
       "1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545\n",
       "1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633\n",
       "1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706\n",
       "1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767\n",
       "2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817\n",
       "2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857\n",
       "2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890\n",
       "2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916\n",
       "2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936\n",
       "2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952\n",
       "2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964\n",
       "2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974\n",
       "2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981\n",
       "2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986\n",
       "3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990\n",
       "3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993\n",
       "3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995\n",
       "3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997\n",
       "3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "standard_normal_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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